Please Help Explain

[Jakle]

I was at a job interview one day and the owner of the start up company asked
me if I'd rather make $1000 dollars a day, or start off with a penny a day
and double the amount every day for 30 days. I was too lazy to sit down with
paper and pen to figure out how much the second choice came out to. But now
I'm learning python and just learned about recursive functions and
iteration, I figured I'd use those theories to figure out the problem. After
racking my brain trying to figure it out (I'm a noob to this stuff, and math
isn't my strong point), I came up with this formula: n = n*2. So I messed
around with it and came up with the following code:

+++++++++++++++++++++++++++++++++++++++
# penny.py 11-05-03

days = raw_input("How many days: ")

def calc(n, days):
i = 1
while i <= days:
n = n*2
i = i+1
return n/float(100)

print calc(1, int(days))
+++++++++++++++++++++++++++++++++++++++

I completely stumbled across it and it works. I just don't understand how
the value of n is assigned to the second n in "n=n*2" once it loops back
again. I would understand if it was a recursive function and passed as an
argument, but I don't think I completely understand how the "while"
statement handles variable values. I am learning from "How to Think Like a
Computer Scientist: Learning With Python", and it doesn't go into too much
depth about it, at the moment at least. I was wondering if anyone could shed
some light on my dilema.

Thanks ahead of time.

 

[Ben Finney]

I was at a job interview one day and the owner of the start up company
asked me if I'd rather make $1000 dollars a day, or start off with a
penny a day and double the amount every day for 30 days.

A classic surprise in mathematics. A doubling series gets large
unexpectedly quickly, until you've seen it happen a few times.

It's the subject of an ancient parable (of Arabic origin, I believe). A
pauper manages to beat the king at chess, and the king condescendingly
offers the pauper a hearty meal as reward. The pauper asks for a more
modest reward: he asks the king to place a single rice grain on the
first square of the board, two on the next, four on the next, eight on
the next, and so on for all sixty-four squares of the chessboard. The
king, believing he can be rid of the pauper for the price of a bowl or
two of rice, agrees. By the end of the exercise, the pauper is owed
enough rice to empty all the royal granaries. (2 to the power 64 is
18,446,744,073,709,551,616.)

The same principle occurs in bacterial infection. A single bacterium
infects the host, and then after a short time divides in two. This is
repeated indefinitely; for a while, the host notices nothing, until
quite suddenly the infection blossoms. The rate of doubling hasn't
altered appreciably; but the increase after the initial slow period is
dramatic.

I was too lazy to sit down with paper and pen to figure out how much
the second choice came out to.

They weren't testing your ability to perform the arithmetic (2 to the
power 30 is 1,073,741,824); they were testing your familiarity with the
principle.

I came up with this formula: n = n*2.

Yep, that's the formula (actually y = x * 2, so that it's clear there's
an old value and a new one).

def calc(n, days):
i = 1
while i <= days:
n = n*2
i = i+1
return n/float(100)

I completely stumbled across it and it works.

Copngratulations (and further points for wanting to understand why it
works).

I just don't understand how the value of n is assigned to the second n
in "n=n*2" once it loops back again.

The assignment conceptually occurs in two steps:

- evaluate ("make a single value from") the right-hand side
- asign the value to the left-hand side

So the evaluation creates a new value that is (n*2). Then, this new
value is assigned to n, and whatever value n held previously is
forgotten. None of this is visible to you; it's all handled by the
Python engine. All you see is the result (that n has the new calculated
value).

I would understand if it was a recursive function and passed as an
argument, but I don't think I completely understand how the "while"
statement handles variable values.

Hopefully this helps resolve the dilemma of a self-referential
assignment.

I am learning from "How to Think Like a Computer Scientist: Learning
With Python"

A good text. Also work through these:

"Python tutorial" (as soon as you can)
<http://www.python.org/doc/tut/>

"Dive Into Python" (when you're ready for some more)
<http://www.diveintopython.org/>

 

[Lucik]

n=0
while you_wish_to_eat
# eat couple of hotdogs
n = n+2
return n # total number of hotdogs

You can not return to the same state in the loop.
Natural and without depth.

 

[Andrei]

Jakle wrote on Thu, 06 Nov 2003 04:01:21 GMT:

I was at a job interview one day and the owner of the start up company asked
me if I'd rather make $1000 dollars a day, or start off with a penny a day
and double the amount every day for 30 days. I was too lazy to sit down with
paper and pen to figure out how much the second choice came out to. But now

You don't really need a special function for that, just the ** operator .

I completely stumbled across it and it works. I just don't understand how
the value of n is assigned to the second n in "n=n*2" once it loops back

This simply is run like this:

- take the value of n
- multiply it with 2
- store the result as n again

It's not trying to both read and assign n at the same time. It's a bit
weird if you look at it from a mathematical standpoint (solve "x=x+2"), but
you shouldn't look at it that way.

--
Yours,

Andrei

=====
Mail address in header catches spam. Real contact info (decode with rot13):
(e-mail address removed). Fcnz-serr! Cyrnfr qb abg hfr va choyvp cbfgf. V
ernq gur yvfg, fb gurer'f ab arrq gb PP.

 

[Stan Graves]

+++++++++++++++++++++++++++++++++++++++
# penny.py 11-05-03

days = raw_input("How many days: ")

def calc(n, days):
i = 1
while i <= days:
n = n*2
i = i+1
return n/float(100)

Technically, the return should be:

return (n-1)/float(100)

The point is to sum the total, and your method over estimates the sum
by 1. You can verify this by running the program for 2 days and
looking at the total.

If the pay is one penny on the first day, and two pennies on the
second day - the the sum at the end of two days is 3 cents...not four
cents as suggested by the above code.

--Stan Graves
(e-mail address removed)
http://www.SoundInMotionDJ.com

 

[JanC]

It's the subject of an ancient parable (of Arabic origin, I believe).

Indian -> Persian -> Arabic

And then it came to the barbaric Western world, together with the chess
game itself... ;-)

 

[Ben Finney]

And then [the doubling parable] came to the barbaric Western world,
together with the chess game itself... ;-)

Meh. I far prefer the game of go these days.

<http://en2.wikipedia.org/wiki/Go_(board_game)>

 

[Timo Virkkala]

And then [the doubling parable] came to the barbaric Western world,
together with the chess game itself... ;-)

Meh. I far prefer the game of go these days.

Go is imperfect. Go with Hex (or Nash, as it was originally known, after
it's inventor John Nash).

=)

 

[Timo Virkkala]

n=0
while you_wish_to_eat
# eat couple of hotdogs
n = n+2
return n # total number of hotdogs

No. The idea was to double the amount, not add 2 to it.

 

[Nick Vargish]

Go is imperfect. Go with Hex (or Nash, as it was originally known,
after it's inventor John Nash).

Can you explain what you mean by imperfect? I assume that's some
mathematical condition?

From a lay-person's view, Hex is less than perfect, since according to
Nash's proof, the first player can always win.

Nick

 

[Jakle]

I want to thank you guys for the input. I want to appologize for taking so
long to respond, I've been at work way too much lately. Thanks again